You will be fine,see my signature my trailer is larger than yours.
2007.5 up 3.73 were only available in the 1500's with the 6.0l vortec max or 6.2L max trailering package.

That is correct through '13 for the GMT-900.

Starting with the new '14 truck (K2000 or whatever it is called), the 1500's were/are available with the 5.3 and max tow package which include the 3.73 gears. With the 6.2 now having the 8spd trans the max tow includes 3.42 gears if I remember correctly.

DeeBee I have the very same trailer and I tow with an 04 Silverado , 5.3l with 3:73 gears. This truck pulls just fine. I was up and down the Berkshire mountains without issues. I've been up and down the Pocono mountains with no issues. Go and enjoy your TT.

Thanks so much everyone for your help! We have a deposit on one of the last 24FBS's coming off the line. They are changing the floorplan and naming it something else. We really like the floorplan of the 24FBS...so hopefully it will all work out! We are excited!!!